A354259 Expansion of e.g.f. 1/sqrt(1 - 6 * log(1+x)).

1, 3, 24, 330, 6354, 157482, 4772268, 170950392, 7066790676, 331108863372, 17340063707952, 1003726452207960, 63635982830437320, 4385439331442232840, 326404115258791793040, 26093904013675118381760, 2229931839713559043435920

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

E.g.f.: Sum_{k>=0} binomial(2*k,k) * (3 * log(1+x)/2)^k.

a(n) = Sum_{k=0..n} (3/2)^k * (2*k)! * Stirling1(n,k)/k!.

a(n) ~ n^n / (sqrt(3) * (exp(1/6)-1)^(n + 1/2) * exp(n - 1/12)). - Vaclav Kotesovec, Jun 04 2022

Mathematica

With[{nn=20}, CoefficientList[Series[1/Sqrt[1-6Log[1+x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 06 2023 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-6*log(1+x))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, binomial(2*k, k)*(3*log(1+x)/2)^k)))
(PARI) a(n) = sum(k=0, n, (3/2)^k*(2*k)!*stirling(n, k, 1)/k!);

Crossrefs

Cf. A320343, A354240, A354260.

Cf. A354252, A354261.

Sequence in context: A319939 A375869 A082166 * A370055 A381443 A380808

Adjacent sequences: A354256 A354257 A354258 * A354260 A354261 A354262

Keyword

nonn

Author

Seiichi Manyama, May 21 2022

Status

approved